It's taking the integral of cos(x)^xFrom your syntax it is not clear if you want to take the integral of cos(x)^x or if you want to take the integral of cos(x) and then raise that to the power of x.
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Maybe, maybe not. I thought of a manipulation:So I conclude there's something wrong with the question itself.
Oh, yes. I see your point. I'm at loss here. What do you suggest?By that logic the integral would be the same as sin(x)^x or frac(x)^x or saw(x)^x or any other function bounded between -1 and 1.
Well, that is the result for integrate[Cos[x]^2,x]use wolfram alpha, but you need the correct syntax.
http://www.wolframalpha.com/input/?i=Integrate[Cos[x]^2,x]